| 乘法半群(S,·)是逆半群的双半环 |
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| 引用本文： | 袁萌,李刚.乘法半群(S,·)是逆半群的双半环[J].山东科学,2018,31(2):100-104. |
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| 作者姓名： | 袁萌 李刚 |
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| 作者单位： | 山东师范大学数学与统计学院, 山东 济南 250014 |
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| 基金项目： | 国家自然科学基金（11601288） |
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| 摘 要： | 本文研究了(S,+)半群为半格、(S,·)半群为逆半群、(S,*)半群为半格的双半环, 利用加法半群(S,+)、乘法半群(S,·)和乘法半群(S,*)上的偏序以及三者之间的关系, 给出了该类双半环成为分配格的几个等价命题。
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| 关 键 词： | 半格 逆半群 分配格 双半环 偏序 |
| 收稿时间： | 2017-04-20 |
Bi-semiring whose multiplicative semigroup(S,·)is an inverse semigroup |
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| YUAN Meng,LI Gang.Bi-semiring whose multiplicative semigroup(S,·)is an inverse semigroup[J].Shandong Science,2018,31(2):100-104. |
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| Authors: | YUAN Meng LI Gang |
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| Institution: | School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China |
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| Abstract: | A bi-semiring whose semigroup S,+ was a semilattice, semigroup S,· was an inverse semigroup and semiroup S,* was a semilattice was studied in this paper. By using three partial orders constructed on S,+,S,· and S,* and the relationships among them, some equivalent statements for this kind of bi semiring to be a distributive lattice were given. |
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| Keywords: | inverse semigroup distributive lattice semilattice partial order bi-semiring |
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